# Pexeso

Drawing paper has dimensions of 60cm and 840mm. Pupils have to divide it into squares so that they can make a pexeso. What dimension must squares have if their side is to be larger than 3cm and less than 10cm?

Correct result:

x1 =  60 mm
x2 =  40 mm

#### Solution:

$a=60 \ cm \rightarrow mm=60 \cdot \ 10 \ mm=600 \ mm \ \\ b=840 \ \text{mm} \ \\ \ \\ 600=2^3 \cdot 3 \cdot 5^2 \ \\ 840=2^3 \cdot 3 \cdot 5 \cdot 7 \ \\ \text{GCD}(600, 840)=2^3 \cdot 3 \cdot 5=120 \ \\ \ \\ y=GCD(a,b)=GCD(600,840)=120 \ \\ \ \\ 30 < x< 100 \ \\ \ \\ x_{1}=y/2=120/2=60 \ \text{mm}$
$x_{2}=y/3=120/3=40 \ \text{mm}$

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